Question: Daniel is 3 years younger than Christopher. Christopher and Daniel first met 3 years ago. Nine years ago, Christopher was 4 times as old as Daniel. How old is Christopher now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Daniel. Let Christopher's current age be $c$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $c = d + 3$ Nine years ago, Christopher was $c - 9$ years old, and Daniel was $d - 9$ years old. The information in the second sentence can be expressed in the following equation: $c - 9 = 4(d - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = c - 3$ . Substituting this into our second equation, we get the equation: $c - 9 = 4($ $(c - 3)$ $ -$ $ 9)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $c - 9 = 4c - 48$ Solving for $c$ , we get: $3 c = 39$ $c = 13$.